On the early history of axiomatics

the interaction of mathematics and philosophy in Greek antiquity

Wilbur Richard Knorr

pp. 81-109

in: Jean Christianidis (ed), Classics in the history of Greek mathematics, Berlin, Springer, 2004

Abstract

The manner of the origins of deductive method both in philosophy and in mathematics has exercised the thoughts of many notable scholars. Unique to the ancient Greek tradition were conscious efforts to comprehend the process of thinking itself, and these inquiries have since developed into the philosophical subfields of logic, epistemology and axiomatics. At the same time, the pre-Euclidean Greek mathematicians turned to the problem of organizing arithmetic and geometry into axiomatic systems, in effect setting a precedent for the field of mathematical foundations. Did these two movements in the history of thought arise independent of each other, through some extraordinary coincidence? It would appear far more likely that this common adoption of deductive method resulted through interaction between the fields of philosophy and mathematics. But if this is so, to which shall we attribute priority?